Just a bit more info on those early morning buses. They do start running at about 6:15-6:30. But, they don't run quite as frequently as the regular park buses...so plan accordingly. If you just miss one, it could be awhile before the next one comes along.
About an hour before the park opens, the buses will start running every 10-15 mins..then once the park is opened, they will run every 15-20 mins...because of less need.